An infinite horizon dynamic optimization problem with constraints and applications to resource extraction problems

I would like to present our research work where we analyse an infinite horizon dynamic optimization problem -- a generalization of a linear quadratic problem with state dependent constraints. This model suits well extraction of renewable resources (e.g. a fishery). The class of sub-problems considered encompasses a linear quadratic optimal control problem as well as models with maximal carrying capacity of the environment. This problem is also interesting from theoretical point of view -- although it seems simple in its linear quadratic form, calculation of the optimal control is nontrivial. Moreover, this problem constitutes a counterexample to at least two methodological approaches often used in applicational papers on optimal control or dynamic games